A study of nonlocal conductivity in high-temperature superconductors

TL;DR

This paper investigates the nonlocal conductivity in high-temperature superconductors, aiming to extract key length scales from transport data despite the inverse problem's complexity and data inconsistencies.

Contribution

It introduces a new, more stable approximation scheme for conductivity analysis that handles both positive and negative viscosity coefficients, improving upon hydrodynamic methods.

Findings

Surface effects significantly influence conductivity.

Positive viscosity coefficients are necessary to match experimental results.

A robust approximation scheme for conductivity analysis is developed.

Abstract

We examine nonlocal conductivity in high-temperature superconductors from a phenomenological point of view. One wants to deduce the properties of the conductivity, especially its inherent length scales, from the transport data. Although this is a challenging inverse problem, complicated further by the experimental data not being completely self-consistent, we have made some progress. We find that if a certain form for the conductivity is postulated then one requires positive "viscosity" coefficients to reproduce some of the experimental results. We are able to show that the effects of surfaces on the conductivity are likely to be important and draw comparisons with the treatment of the surface within the hydrodynamic approach put forth by Huse and Majumdar. We also develop an approximation scheme for the conductivity which is more robust than the hydrodynamic one, since it is stable for both positive and negative viscosity coefficients, and discuss the results obtained using it.